The BA model explained successfully the observed scale–free nature of many
networks by the “rich-gets-richer” phenomenon. However, the model was too
simple to fit most measured quantities of the real Internet. For example, the
degree scaling-exponent in (REF ) is \(\delta _{\mathrm {BA}}=3\) 
which is in contrast with the exponent \(\delta =2.15\) –\(2.2\)  observed in
Internet measurements
[1]}, [2]}. The BA
model was later refined by a number of other authors.
[3]} studied the aging of nodes. The authors extended
the BA preferential attachment rule so that attachment probability was
proportional not only to the degree, but also to \((t-t_i)^{-\nu }\) , a power law
function of age, where \(\nu \)  is a tunable parameter. It has been shown
analytically and by simulation that the scale-free structure of the network
disappears if \(\nu >1\) . Moreover, an implicit equation was derived
between the scaling exponent of the degree distribution and \(\nu \)  for
\(-\infty <\nu <1\) . The influence of exponentially fast aging on global and local
clustering, degree–degree correlation and the diameter of the network was
analyzed by [4]}.
